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We introduce and study a class of optimization problems we call replenishment problems with fixed turnover times: a very natural model that has received little attention in the literature. Clients with capacity for storing a certain commodity are located at various places; at each client the commodity depletes within a certain time, the turnover time, which is constant but can vary between locations. Clients should never run empty. The natural feature that makes this problem interesting is that we may schedule a replenishment (well) before a client becomes empty, but then the next replenishment will be due earlier also. This added workload needs to be balanced against the cost of routing vehicles to do the replenishments. In this paper, we focus on the aspect of minimizing routing costs. However, the framework of recurring tasks, in which the next job of a task must be done within a fixed amount of time after the previous one is much more general and gives an adequate model for many practical situations. Note that our problem has an infinite time horizon. However, it can be fully characterized by a compact input, containing only the location of each client and a turnover time. This makes determining its computational complexity highly challenging and indeed it remains essentially unresolved. We study the problem for two objectives: min–avg minimizes the average tour cost and min–max minimizes the maximum tour cost over all days. For min–max we derive a logarithmic factor approximation for the problem on general metrics and a 6-approximation for the problem on trees, for which we have a proof of NP-hardness. For min–avg we present a logarithmic factor approximation on general metrics, a 2-approximation for trees, and a pseudopolynomial time algorithm for the line. Many intriguing problems remain open.

The algorithm-design paradigm of algorithms using predictions is explored as a means of incorporating the computations of lower-assurance components (such as machine-learning based ones) into safety-critical systems that must have their correctness validated to very high levels of assurance. The paradigm is applied to two simple example applications that are relevant to the real-time systems community: energy-aware scheduling, and classification using ML-based classifiers in conjunction with more reliable but slower deterministic classifiers. It is shown how algorithms using predictions achieve much-improved performance when the low-assurance computations are correct, at a cost of no more than a slight performance degradation even when they turn out to be completely wrong., LIPIcs, Vol. 262, 35th Euromicro Conference on Real-Time Systems (ECRTS 2023), pages 3:1-3:19

We consider the problem of constructing strings over an alphabet Σ that start with a given prefix u, end with a given suffix v, and avoid occurrences of a given set of forbidden substrings. In the decision version of the problem, given a set S_k of forbidden substrings, each of length k, over Σ, we are asked to decide whether there exists a string x over Σ such that u is a prefix of x, v is a suffix of x, and no s ∈ S_k occurs in x. Our first result is an 𝒪(|u|+|v|+k|S_k|)-time algorithm to decide this problem. In the more general optimization version of the problem, given a set S of forbidden arbitrary-length substrings over Σ, we are asked to construct a shortest string x over Σ such that u is a prefix of x, v is a suffix of x, and no s ∈ S occurs in x. Our second result is an 𝒪(|u|+|v|+||S||⋅|Σ|)-time algorithm to solve this problem, where ||S|| denotes the total length of the elements of S. Interestingly, our results can be directly applied to solve the reachability and shortest path problems in complete de Bruijn graphs in the presence of forbidden edges or of forbidden paths. Our algorithms are motivated by data privacy, and in particular, by the data sanitization process. In the context of strings, sanitization consists in hiding forbidden substrings from a given string by introducing the least amount of spurious information. We consider the following problem. Given a string w of length n over Σ, an integer k, and a set S_k of forbidden substrings, each of length k, over Σ, construct a shortest string y over Σ such that no s ∈ S_k occurs in y and the sequence of all other length-k fragments occurring in w is a subsequence of the sequence of the length-k fragments occurring in y. Our third result is an 𝒪(nk|S_k|⋅|Σ|)-time algorithm to solve this problem., LIPIcs, Vol. 191, 32nd Annual Symposium on Combinatorial Pattern Matching (CPM 2021), pages 9:1-9:18

We propose a model for scheduling jobs in a parallel machine setting that takes into account the cost of migrations by assuming that the processing time of a job may depend on the specific set of machines among which the job is migrated. For the makespan minimization objective, the model generalizes classical scheduling problems such as unrelated parallel machine scheduling, as well as novel ones such as semi-partitioned and clustered scheduling. In the case of a hierarchical family of machines, we derive a compact integer linear programming (ILP) formulation for the job assignment subproblem, and show how to turn arbitrary ILP solutions into valid schedules. We also derive a polynomial-time 2-approximation algorithm for the problem. Extensions that incorporate memory capacity constraints are also discussed.

The growing need to deal with massive instances motivates the design of algorithms balancing the quality of the solution with applicability. For the latter, an important measure is the \emph{adaptive complexity}, capturing the number of sequential rounds of parallel computation needed. In this work we obtain the first \emph{constant factor} approximation algorithm for non-monotone submodular maximization subject to a knapsack constraint with \emph{near-optimal} $O(\log n)$ adaptive complexity. Low adaptivity by itself, however, is not enough: one needs to account for the total number of function evaluations (or value queries) as well. Our algorithm asks $\tilde{O}(n^2)$ value queries, but can be modified to run with only $\tilde{O}(n)$ instead, while retaining a low adaptive complexity of $O(\log^2n)$. Besides the above improvement in adaptivity, this is also the first \emph{combinatorial} approach with sublinear adaptive complexity for the problem and yields algorithms comparable to the state-of-the-art even for the special cases of cardinality constraints or monotone objectives. Finally, we showcase our algorithms' applicability on real-world datasets.

The 19th ATMOS symposium (ATMOS’19) was held in connection with ALGO’19and hosted by Technische Universität München in Munich, Germany, on September 12-13,2019. Topics of interest were all optimization problems for passenger and freight transport,including, but not limited to, demand forecasting, models for user behavior, design of pricing systems, infrastructure planning, multi-modal transport optimization, mobile applications for transport, congestion modelling and reduction, line planning, timetable generation, routing and platform assignment, vehicle scheduling, route planning, crew and duty scheduling,rostering, delay management, routing in road networks, and traffic guidance.

Feasibility analysis for Conditional DAG tasks (C-DAGs) upon multiprocessor platforms is shown to be complete for the complexity class pspace. It is shown that as a consequence integer linear programming solvers (ILP solvers) are likely to prove inadequate for such analysis. A demarcation is identified between the feasibility-analysis problems on C-DAGs that are efficiently solvable using ILP solvers and those that are not, by characterizing a restricted class of C-DAGs for which feasibility analysis is shown to be efficiently solvable using ILP solvers., LIPIcs, Vol. 196, 33rd Euromicro Conference on Real-Time Systems (ECRTS 2021), pages 12:1-12:17

International audience; As parallel processing became ubiquitous in modern computing systems, parallel task models have been proposed to describe the structure of parallel applications. The workflow scheduling problem has been studied extensively over past years, focusing on multiprocessor systems and distributed environments (e.g. grids, clusters). In workflow scheduling, applications are modeled as directed acyclic graphs (DAGs). DAGs have also been introduced in the real-time scheduling community to model the execution of multi-threaded programs on a multi-core architecture. The DAG model assumes, in most cases, a fixed DAG structure capturing only straight-line code. Only recently, more general models have been proposed. In particular, the conditional DAG model allows the presence of control structures such as conditional (if-then-else) constructs. While first algorithmic results have been presented for the conditional DAG model, the complexity of schedulability analysis remains wide open. We perform a thorough analysis on the worst-case makespan (latest completion time) of a conditional DAG task under list scheduling (a.k.a. fixed-priority scheduling). We show several hardness results concerning the complexity of the optimization problem on multiple processors, even if the conditional DAG has a well-nested structure. For general conditional DAG tasks, the problem is intractable even on a single processor. Complementing these negative results, we show that certain practice-relevant DAG structures are very well tractable.

International audience; The problem of partitioning systems of independent constrained-deadline sporadic tasks upon heterogeneous multiprocessor platforms is considered. Several different integer linear program (ILP) formulations of this problem, offering different tradeoffs between effectiveness (as quantified by speedup bound) and running time efficiency, are presented. One of the formulations is leveraged to improve the best speedup guarantee known for a polynomial-time partitioning algorithm , from 12.9 to 7.83. Extensive computational results on synthetically generated instances are also provided to establish the effectiveness of the ILP formulations .

Motivation Analysis of differential expression of genes is often performed to understand how the metabolic activity of an organism is impacted by a perturbation. However, because the system of metabolic regulation is complex and all changes are not directly reflected in the expression levels, interpreting these data can be difficult. Results In this work, we present a new algorithm and computational tool that uses a genome-scale metabolic reconstruction to infer metabolic changes from differential expression data. Using the framework of constraint-based analysis, our method produces a qualitative hypothesis of a change in metabolic activity. In other words, each reaction of the network is inferred to have increased, decreased, or remained unchanged in flux. In contrast to similar previous approaches, our method does not require a biological objective function and does not assign on/off activity states to genes. An implementation is provided and it is available online. We apply the method to three published datasets to show that it successfully accomplishes its two main goals: confirming or rejecting metabolic changes suggested by differentially expressed genes based on how well they fit in as parts of a coordinated metabolic change, as well as inferring changes in reactions whose genes did not undergo differential expression. Availability and implementation github.com/htpusa/moomin. Supplementary information Supplementary data are available at Bioinformatics online.

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Sorting with stacks is a collection of problems that deal with sorting a sequence of numbers by pushing and popping the numbers to and from a given set of stacks. Multiple concrete decision or optimization questions are formed by restricting the access to the stacks. The motivation comes, e.g., from shunting train wagons in shunting yards, shunting trams in depots, or in stacking cargo containers on cargo ships or storage yards in transshipment terminals. We consider the problem of sorting a permutation of n integers 1, 2, . . ., n using k ≥ 2 stacks. In this problem, elements from the input sequence are pushed one-by-one (in the order of the elements in the sequence) to one of the k stacks. At any time, an element from a stack can be popped and pushed to another stack; such an operation is called a shuffle. Also, at any time, an element can be popped from a stack and placed to the output sequence. We can only place the elements to the output in the increasing order of their value such that at the end the output is the ordered sequence of the elements. The problem asks to minimize the number of shuffles in the process. It is known that for k ≥ 4, the problem is NP-hard, and that there is no approximation algorithm unless P=NP. For k ≥ 3, it is known that at most O(n log n) shuffles are needed for any input sequence. For the case when k = 2, there exist input sequences that require Ω(n 2− ε) shuffles, for any ε > 0. Nothing substantially more is known for the case of k = 2. In this paper, we study the following variant of the problem with k = 2 stacks: no shuffle and no placement to the output sequence can happen before every element is in one of the two stacks. We show that our problem can be seen as the MinUnCut problem by providing a polynomial-time reduction, and thus we show that there exists a randomized O(√log n)-approximation algorithm and a deterministic O(log n)-approximation algorithm for our problem.

International audience; Recent technological advances have led to an increasing gap between memory and processor performance, since memory bandwidth is progressing at a much slower pace than processor bandwidth. Pre-fetching techniques are traditionally used to bridge this gap and achieve high processor utilization while tolerating high memory latencies. Following this trend, new computational models have been proposed to split task execution in two consecutive phases: a memory phase in which the required instructions and data are pre-fetched to local memory (M-phase), and an execution phase in which the task is executed with no memory contention (C-phase). Decoupling memory and execution phases not only simplifies the timing analysis, but also allows a more efficient (and predictable) pipelining of memory and execution phases through proper co-scheduling algorithms. This paper takes a further step towards the design of smart co-scheduling algorithms for sporadic real-time tasks complying with the memory-computation (M/C) model, by proposing a theoretical framework aimed at tightly characterizing the schedulability improvement obtainable with the adopted M/C task model on single-core systems. In particular, a critical instant is identified for M/C tasks scheduled with fixed priority and an exact response time analysis with pseudo-polynomial complexity is provided. Then, we investigate the problem of priority assignment for M/C tasks, showing that a necessary condition to achieve optimality is to allow different priorities for the two phases. Our experiments show that the proposed techniques provide a significant schedulability improvement with respect to classic execution models, placing an important building block towards the design of more efficient partitioned multi-core systems.